Electronics Components: Combine Resistors in Series and Parallel

There are two basic ways to combine resistors in an electronic circuit: in series (strung end to end) and in parallel (side by side). The following explains how you calculate the total resistance of a network of resistors in series and in parallel.

You'll need to put your thinking cap on when you do the math calculations required to calculate parallel resistors. The math isn't horribly complicated, but it isn't trivial, either.

Combine resistors in series

Calculating the total resistance for two or more resistors strung end to end — that is, in series — is simple: You simply add the resistance values to get the total resistance.

For example, if you need 1,100 ohms of resistance and can't find an 1,100 Ω resistor, you can combine a 1,000 Ω resistor and a 100 Ω resistor in series. Adding these two resistances together gives you a total resistance of 1,100 Ω.

You can place more than two resistors in series if you want. You just keep adding up all the resistances to get the total resistance value. For example, if you need 1,800 Ω of resistance, you could use a 1 kΩ resistor and eight 100 Ω resistors in series.

Here, the two circuits have identical resistances. The circuit on the left accomplishes the job with one resistor; the circuit on the right does it with three. Thus, the circuits are equivalent.

Any time you see two or more resistors in series in a circuit, you can substitute a single resistor whose value is the sum of the individual resistors. Similarly, any time you see a single resistor in a circuit, you can substitute two or more resistors in series as long as their values add up to the desired value.

The total resistance of resistors in series is always greater than the resistance of any of the individual resistors. That's because each resistor adds its own resistance to the total.

Combine resistors in parallel

You can also combine resistors in parallel to create equivalent resistances. However, calculating the total resistance for resistors in parallel is a bit more complicated than calculating the resistance for resistors in series.

When you combine two resistors in parallel, current can flow through both resistors at the same time. Although each resistor does its job to hold back the current, the total resistance of two resistors in parallel is always less than the resistance of either of the resistors because the current has two pathways through which to go.

So how do you calculate the total resistance for resistors in parallel? Very carefully. Here are the rules:

First, the simplest case: Resistors of equal value in parallel. In this case, you can calculate the total resistance by dividing the value of one of the individual resistors by the number of resistors in parallel. For example, the total resistance of two, 1 kΩ resistors in parallel is 500 Ω and the total resistance of four, 1 kΩ resistors is 250 Ω.

Unfortunately, this is the only case that's simple. The math when resistors in parallel have unequal values is more complicated.

If only two resistors of different values are involved, the calculation isn't too bad:

In this formula, R1 and R2 are the values of the two resistors.

Here's an example, based on a 2 kΩ and a 3 kΩ resistor in parallel:

For three or more resistors in parallel, the calculation begins to look like rocket science:

The dots at the end of the expression indicate that you keep adding up the reciprocals of the resistances for as many resistors as you have.

In case you're crazy enough to actually want to do this kind of math, here's an example for three resistors whose values are 2 kΩ, 4 kΩ, and 8 kΩ:

As you can see, the final result is 1,142.857 Ω. That's more precision than you could possibly want, so you can probably safely round it off to 1,142 Ω, or maybe even 1,150 Ω.